Constant quality factor transform (CQT)

Principle

The constant constant quality factor transform (CQT),
introduced by J.C. Brown in 1988 (see references), is an interesting
alternative to the windowed Fourier transform (STFT / Short Time Fourier Transform)
or wavelets, for time-frequency analysis, particularly in the field of audio applications.

Indeed, for such applications, the reference metric is defined by the capabilities
of the human ear, and since we perceive sounds by a physical system that
can be modeled by a bank of almost constant Q filters, where what
we call 'quality factor' (Q) is the ratio of the width of
the filter against the center frequency: Q = df / f.
In other words, at low frequencies, we are capable of very fine frequency
resolution (a few Hz at 1000 Hz) and at high frequency we are much less
accurate (a few tens of Hz at 10 KHz).

SCILAB script API

The Scilab script you can find here (see link at right) offers two functions: